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arXiv · 1204.0087

Ramanujan type congruences for modular forms of several variables

Toshiyuki Kikuta·Shoyu Nagaoka
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Abstract

We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the $k-1$-th generalized Bernoulli number and the existence of non-trivial Hermitian cusp forms of weight $k$. We will conclude by giving numerical examples for each case.

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Toshiyuki Kikuta, Shoyu Nagaoka. 2012-03-31. Ramanujan type congruences for modular forms of several variables. https://arxiv.org/abs/1204.0087

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